The least squares coefficients are given by [math]\hat{\beta} = (X^TX)^{-1}X^{T}y[/math], and we assume that [math]y = X\beta + \epsilon[/math]. If we take [math]X[/math] to be constant and [math]\epsilon[/math] to be normally distributed, then it follows immediately that [math]\hat{\beta}[/math] is also normally distributed.